Can quantum algorithms revolutionise the simulation of turbulent flows?

我们的研究愿景是创建一个框架和工具箱，将60多年的高性能计算与量子计算相结合，以彻底改变对流体力学的理解，建模和模拟。风力发电场的高效能量转换、超新星爆炸以及飞机周围的空气阻力都有一个共同的因素：流体。流体力学是英国主要的工业和研究力量，是交通，医疗保健，海洋和能源的一项使能技术。根据2021年英国白色文件，流体机械是一个在2,200家公司雇用45,000人的部门，为英国创造了140亿英镑的产出。实际感兴趣的流体可以是湍流的。在基础研究和应用研究中，数值模拟是理解、预测和控制湍流的关键。在基础研究中，目标是揭示湍流的物理机制，尺度和动力学。在工业中，目标是将湍流的精确数值模拟嵌入到工程设计周期中。虽然我们知道一个很好的湍流模型（Navier-Stokes方程），但湍流的混沌性质使得精确的计算机模拟非常昂贵。例如，一个简单的槽道流湍流的最先进的模拟需要3500亿个网格点，需要2.6亿个计算小时。为了分析基本和工程配置，部署了大型超级计算资源。虽然计算机的浮点运算大约每两年翻一番，但我们需要等待几十年才能以现实的流速处理基本流，如通道流。然而，下一代的大型艾级计算机只允许流速比最先进的计算机增加三到五倍。问题是“我们如何能够用负担得起的计算准确地模拟实际感兴趣的湍流？“经典的算法已经达到了极限。这一提议的关键是观察到湍流的非线性方程的数值解围绕着求解线性系统。线性系统可以通过量子算法以惊人的速度求解。量子计算提供了一个算法库，可以彻底改变计算科学和湍流模拟。这是因为经典计算机需要的计算资源随着系统的自由度呈指数级扩展，而量子算法只按多项式扩展。这也被称为量子优势。如果谷歌、微软、IBM、麻省理工学院、哈佛等公司在2021年发表的关于量子优势的论文是正确的，那么对湍流系统的模拟可以加速十到一千个数量级。该项目将开拓这一研究领域。在这个项目中，我们将开发和测试量子增强计算流体动力学（q-CFD）通过利用未经测试的，但合理的，量子优势。这将为经典和量子算法的协同组合计算湍流开辟道路。

Our research vision is to create a framework and toolbox to marry over 60 years of high-performance computing with quantum computing to revolutionise understanding, modelling, and simulation of fluid mechanics. The efficient conversion of energy in wind farms, the explosions of supernovas, and the air resistance around airplanes have a common factor: a fluid. Fluid mechanics is a major UK industrial and research strength, which is an enabling technology from transport, healthcare, marine and energy. According to the 2021 UK white paper, fluid mechanics is a sector that employs 45,000 people in 2,200 companies, which generates a £14-billion output to the UK. Fluids of practical interest can be turbulent. Both in fundamental and applied research, numerical simulation is key to understanding, predicting and controlling turbulent flows. In fundamental research, the goal is to unveil the physical mechanisms, scales and dynamics of turbulence. In industry, the goal is to embed accurate numerical simulations of turbulence with a fast turnaround into the engineering design cycle. We are far from achieving this.Although we know an excellent model for turbulent flows (the Navier-Stokes equations), the chaotic nature of turbulence makes accurate computer simulations exceedingly expensive. For example, a state-of-the-art simulation of turbulence of a simple channel flow needs 350 billion grid points and takes 260 million computing hours. To analyse fundamental and engineering configurations, large supercomputing resources are deployed. Although the flop operations of computers roughly double every two years, we will need to wait for decades before being able to tackle a fundamental flow, such as a channel flow, at realistic flow velocities. The next generation of large exascale computers, however, will only allow for a three- to five-fold increase in the flow velocities with respect to the state-of-the-art. The question is "how can we accurately simulate turbulent flows of practical interest with affordable computations?" Classical algorithms are reaching their limits.Key to this proposal is the observation that the numerical solution of the nonlinear equations of turbulence revolves around solving linear systems. Linear systems can be solved formidably fast by quantum algorithms. Quantum computing offers a repository of algorithms that can revolutionise computational science and turbulence simulations. This is because classical computers require computational resources that scale exponentially with the system's degrees of freedom, whereas quantum algorithms scale only polynomially. This is also known as the quantum advantage. If the conjectures published in 2021 by Google, Microsoft, IBM, MIT, Harvard, among others, on the quantum advantage are correct, the simulation of a turbulent system can be accelerated by ten to thousand orders of magnitudes. This project will pioneer this research field. In this project, we will develop and test quantum-enhanced computational fluid dynamics (q-CFD) by exploiting the untested, but plausible, quantum advantage. This will blaze the trail for computing turbulence with a synergistic combination of classical and quantum algorithms.